Erasmus+ Project- Hooked on Mathematics

1. Combinatorics
8th November 2018
Class: 9b

2. Aims:
 This lesson looks at the branch of mathematics known as
combinatorics. The students will be given the definition of
combinatorics as well as some of its history and how it is used today.
They will discover exciting examples of things they can count or
arrange in unconventional way.

3. • Activities:
• Definition
 Combinatorics is an aria of
mathematics primarily concerned
with counting, both as a means and
an end in obtaining results, and
certain properties of finite
structures. It is closely related to
many other areas of mathematics
and has many applications ranging
from logic to statistical physics,
from evolutionary biology to
computer science.
• History
 First combinatorial problems have
been studied by ancient Indian,
Arabian and Greek
mathematicians. Interest in the
subject increased during the 19th
and 20th century. Some of the
leading mathematician include
Blaise Pascal /1623-1662/, Jacob
Bernoulli /1654-1705/ and
Leonhard Euler /1707-1783/.

4. • Categories of combinatorics :
permutations, variations, combinations
Definition of permutation
 Permutation is one of the various
ways in which a number of things
can be ordered or arranged. It is
a sequence containing each
element from a finite set of n
elements once, and only once.
Permutations of the same set
differ just in the order of
elements.
Formula of permutation
Pn=n!

5. • Examples
1. In how many ways can five
boys and four girls be
arranged in a line so that each
girl would be between two
boys?
 Solution:
P4.P5 = 4! 5!
2. How many four-digit numbers
containing only once the digits
1,2,3 and 4 are there?
 Solution:
P4 = 4! = 4.3.2.1 = 24

6. 3. Eight students should be accommodated in two three-bed and one two-
bed rooms. In how many ways can they be accommodated?
 Solution:
Room #1: n1 = 3
Room #2: n2 = 3
Room #3: n3 = 2
N = 3+3+2 = 8
P 3,3,2 (8) = 8!
3!3!2!
P 3,3,2 (8) = 40320
72
P 3,3,2 (8) = 560
There are 560 ways of accommodating the students.